%I #7 Jun 13 2015 00:55:26
%S 0,3,23,72,169,321,551,864,1285,1815,2484,3289,4263,5400,6736,8262,
%T 10018,11990,14222,16698,19464,22500,25857,29511,33516,37845,42555,
%U 47616,53089,58939,65231,71928,79097,86697,94800,103361,112455,122034,132176,142830
%N Number of partitions of 7n into exactly 4 parts.
%H Colin Barker, <a href="/A256329/b256329.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).
%F G.f.: x*(x^8+14*x^7+38*x^6+67*x^5+80*x^4+74*x^3+46*x^2+20*x+3) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)).
%e For n=1 the 3 partitions of 7*1 = 7 are [1,1,1,4], [1,1,2,3] and [1,2,2,2].
%o (PARI)
%o concat(0, vector(40, n, k=0; forpart(p=7*n, k++, , [4,4]); k))
%o (PARI)
%o concat(0, Vec(x*(x^8+14*x^7+38*x^6+67*x^5+80*x^4+74*x^3+46*x^2+20*x+3) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))
%Y Cf. A256327 (5n), A256328 (6n).
%K nonn,easy
%O 0,2
%A _Colin Barker_, Mar 25 2015